A numerical implementation of the
Somigliana identity in displacements for the solution
of 3D elastic problems in exponentially
graded isotropic solids is presented. An expression
for the fundamental solution in displacements,
Uj , was deduced by Martin et al. (Proc.
R. Soc. Lond. A, 458, pp. 1931–1947, 2002).
This expression was recently corrected and implemented
in a Galerkin indirect 3D BEM code
by Criado et al. (Int. J. Numer. Meth. Engng.,
2008). Starting from this expression of Uj , a new
expression for the fundamental solution in tractions
Tj has been deduced in the present work.
These quite complex expressions of the integral
kernels Uj and Tj have been implemented in a
collocational direct 3D BEM code. The numerical
results obtained for 3D problems with known
analytic solutions verify that the new expression
for Tj is correct. Excellent accuracy is obtained
with very coarse boundary element meshes, even
for a relativelyMinisterio de Educación Cultura y Deporte SAB2003-0088Ministerio de Ciencia y Tecnología MAT2003-0331
